My one problem with this is the assumption that the time traveling HAD to come after getting an exo body, I mean couldn't you make time travel, time travel to a time you could get an exo body- and then time travel some more.
Or am I missing some detail that would render it impossible for one individual to use a different body then resume time traveling as they did as a human (aka is time traveling tied to the body or a transferable device? Because you did mention different people using the timeline device)
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Sorry, missed this comment earlier. Humans who used the time device had very adverse effects. Some went insane, committed suicide, some even died in the device. Human minds were too weak. The warminds created a drug to try to counteract these effects, and it didn't work. So the scientist realized something else was needed, aka exos. That is why it is assumed the exo stranger needed to be exo before becoming a time traveler